Latin squares, partial latin squares and its generalized quotients

2003/03/27 by Lev Glebsky, L. Yu. Glebsky, Carlos Rubio‐Terres +3
Computer Science · Engineering · Mathematics · #05B15 #05B20 #05C65 #05D15 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems #math.CO #msc:05B15 #msc:05B20 #msc:05C65 #msc:05D15

paper · pdf · doi:10.48550/arxiv.math/0303356

8 pages, 2 figures

arxiv created 2003/03/27 · openalex publication_date 2003/03/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A (partial) Latin square is a table of multiplication of a (partial) quasigroup. Multiplication of a (partial) quasigroup may be considered as a set of triples. We give a necessary and sufficient condition when a set of triples is a quotient of a (partial) Latin square.

Related

• Some existence problems regarding partial Latin squares
• Completing Partial Latin Squares - Alternative Proof
• Quasi-transversal in Latin Squares
• Completing partial Latin squares with two filled rows and three filled columns
• Latin bitrades derived from quasigroup autoparatopisms